Design and Fabrication of Pneumatically Actuated Mars ...

2010 COSGC Space Research Symposium

FROGGER: Design and Fabrication of Pneumatically Actuated Mars Exploration Rover

Stacy Jonett, Joseph Kennedy, Tim Schneider, Ian Smith

Colorado State University Dr. Azar Yalin; Grant Rhodes [email protected]

April 17th, 2010

Abstract Owing to the difficulties encountered by NASA in trying to liberate the Mars rover Spirit, which had become stuck in sand earlier last summer, a Colorado State University DemoSAT team elected to design, fabricate and test a jumping Mars rover. The goal was to demonstrate pneumatic actuators as a viable method for the dislodgment of rovers in unpredictable terrain. The team focused on a hybrid rover having wheels to navigate terrain but also with an on board pneumatic system to launch itself to a height of approximately one meter as could be needed in precarious situations. A preliminary design was developed and fabricated from the results of calculations and experiments. The initial Frogger unit with weight of thirty pounds could jump to a height of 2.5 feet with a gage air pressure of ninety psi. Currently, Frogger is undergoing major redesign in an attempt to reduce mass and improve reliability. 1. Introduction

The purpose of this Mars rover prototype is to prove that pneumatic actuators are a viable option for dislodging Mars rovers in unpredictable terrain. The idea of developing a pneumatically actuated Mars rover was selected after learning of the difficulties encountered by NASA in trying to liberate the Mars rover Spirit, which had become stuck in sand during the summer of 2008 The group decided to look into the possibility of using the thin Martian atmosphere, consisting of mainly carbon dioxide, as a resource to benefit the rovers. On Mars, a rover could use solar or nuclear power to compress the thin CO2 atmosphere, as shown in figure 1, into large pressure reservoirs. These pressure tanks could then be used to power pneumatic actuators that would dislodge a rover if it were to become stuck like Spirit.

2. Project Requirements To design a pneumatic prototype the DemoSAT team

first had to develop and define realistic requirements in order to define concept viability and they were as follows:

PRIMARY OBJECTIVE The rover will jump a minimum of 1 meter on earth:

This requirement will sufficiently demonstrate that the pneumatics system is capable of propelling the rover to a height many times higher than what is necessary to simply dislodge the rover if it were to become stuck. It will also show that the rover design is capable of withstanding the impacts from landing. SECONDARY OBJECTIVES

The rover will drive at least ¼ mile on a single battery charge: The budget for this prototype did not allow for solar panel integration or other alternative power generation. A DC motor driven system was used because the rover will not consume excessive amounts of power during normal operation.

The rover will navigate inclines of at least 45 degrees: This was to measure the rover’s ability to navigate through tough terrain. By designing the rover with enough torque and traction to lift itself up steep inclines, it is more likely to be able to navigate over obstacles, such as rocks, without difficulty.

The rover will drive at a minimum speed of 3 in/s on flat ground: This specification was chosen based on the top speed of the current Mars rovers, Spirit and Opportunity, which travel at 2 in/s. A 50% increase in speed was chosen due to the reduced size and lack of additional payload of the prototype.

Figure 1: Mars with thin CO2 atmosphere visible


3. Original Rover Design

In the original rover design the team focused on the development of five major systems in order to meet all criteria. These systems were categorized as the pneumatic system, the electronic control system, the drive train system, the suspension system, and the frame and balance system.

The pneumatic system dealt primarily with the placement, size, and quantity of the actuators. Electronic systems focused primarily on the integration and timing of the drive systems and pneumatic systems into a remote control unit. The drive system focused on the number of motors and type of wheel motion. Both a tank tread and conventional wheel design were considered with tank treads being the final choice in the original design due to the rough Martian terrain. In addition to the rough terrain, the impact forces that are associated with a “jumping” rover dictated that the rover has a robust internal suspension system in all three axes in order to support the more sensitive components such as the electronics and pneumatics. All of these systems need to be accommodated in a strong, but relatively lightweight and compact frame. Given the possibility that after the launch the rover could land either right side up or upside down, it was decided to design the rover to work in either orientation.

During the design process, weight was a large concern. Many of the simple components could only be purchased as-is, restricting weight control. To compensate, most of the parts were custom manufactured, including the wheels and pneumatic actuators, to reduce weight in those areas.

Due to the lack of an external suspension system, the frame, wheels, and two drive motors received the majority of the impact forces during landing. To compensate, these components were made larger and stronger, but also heavier. A table of the original rover’s major components and their weight allocations can be seen in Table 1.

After a weight estimate was calculated, the actuator’s force, drive motor torque, suspension spring stiffness, and component strength was adjusted accordingly. This was mostly an iterative process, but detailed calculations of actuator design, suspension spring selection, motor and battery selection, and frame strength can be found in the appendices.

3.1. Pneumatic Actuator Design

Actuator orientations were analyzed base on a one, two, or four actuator system. Using only one centralized actuator, launch stability had a high probability of being sacrificed, and four corner pinned actuators would significantly complicate the design and manufacturing as well as add unnecessary weight.

Therefore, a two in-line actuator system was developed along the center of the rover, with the center of gravity at the approximant midpoint. The actuators were designed to fit an arbitrarily set rover size. This design attempted to maximize the stroke length and bore size given the set size of the rover. The largest size actuator that could be accommodated was a 1.875 inch diameter cylinder with a stroke length of four inches. At that size, a calculated pressure of about 90 psi would be required to launch the rover 1 meter. Taking these values as constants, failure modes were determined and components were sized and given relatively large safety factors to prevent possibly dangerous failures of the high pressure actuators. The actuators were then manufactured and assembled for preliminary testing to verify they functioned as predicted. The original design can be seen in Figure 2.

Component Weight (lbs) Center Support Bars and Actuator Tilt Drive Assy.

6.1

Wheels (4) 4.3 Frame 4.2 Pneumatic Actuators (2) 3.1 Batteries 2.7 Valves and Fittings 2.2 Suspension Springs 1.9 Drive Motors (2) 1.6 Compressor 1.0 Drive Belts (2) 0.4 Tank 0.3 Roller Chain 0.1 Total Weight 27.9

Table 1: Component Weight Budget


3.2. Electronics Design

The main emphasis of the project was to demonstrate the use of pneumatics in a Mars rover therefore the electrical design was kept relatively simple. While the rover was not made to be autonomous, electrical components were still needed to interface the rover’s functions to a remote control. For each motor, high current H-bridges were designed and built by soldering four bipolar junction transistors (BJT) onto custom etched circuit board. The two valves are also triggered using high-current BJTs. Short programs were written in Basic to interface these functions with the remote allowing for drive, actuator tilt, and actuator launch controls. Figure 3 shows a functional block diagram.

3.3. Power train Design

Two designs were investigated for the power train design; a track-and-wheel combination verses a 2-wheel drive system. The track-and-wheel combination was the preferred driving method because of the ability to utilize slip steering and the added benefit of increased traction.

After several tests using gears, belts, and a chain and sprocket driven system, the chain drive proved to be the most effective option for power transmission providing a reliable and durable way to transmit power to the wheels, without slip, while allowing for a gear reduction. An example of the chain and sprocket transmission system can be seen in Figure 4.

A two motor combination was selected, as opposed to four motors because of cost and weight efficiency. The motors were selected using three criteria: weight, current draw, and stall torque. The weight and nominal current draw was to be kept as low as possible for the purpose of long range use and power efficiency. A torque large enough to theoretically drive the rover up a 90 degree incline was chosen so that the rover would have plenty of power to climb hills. Matching the speed of 3 in/s was not a limiting factor and was easily surpassed.

Power was supplied by three-eight AA packs battery packs wired in parallel due to ease of replacement and its light weight.

Figure 3: Functional Block Diagram Figure 4: Picture of the rover’s motor, chain drive, and wheel with the track removed.

Figure 2: CAD model of the pneumatic actuator design to launch the rover to a height of 1 meter.


3.4. Suspension Design

To provide suspension to critical components in all three axes, a three dimensional mass and spring design was adapted. Several variations of this design were discussed with the final consensus being that an internal system would be better than having an external system. This decision was based on the fact that if the springs were on the frame, they would be subject to direct impact during some landing scenarios, possibly damaging the springs and impairing their functionality. The tradeoff was that the pneumatics and electronics systems must now be separated into two separate “bays” on each side of a suspension component that goes directly down the middle of the rover (See Figure 5), while avoiding the actuators that are also in this area. The springs were sized according to the estimated weight so that the suspended components would be cushioned by the springs for any fall under 3 feet without the springs fully compressing.

3.5. Frame and System Layout Design

The original frame design was developed to maximize the frame’s strength while minimizing its weight. Again, due to no external suspension system the frame needed a high level of strength to endure impact forces. The wheels were slightly offset from the frame for a more compact design as shown above in Figure 5.

The pneumatic and electronic components are mounted together, and suspended by springs and designed to translate in any direction. Extra space is necessary to prevent these components from colliding with the ground or with the frame during spring compression. In addition, these components also need to be positioned to keep the keep the center of gravity directly between the two actuators.

4. Testing Results

Repeated testing was performed in parallel with manufacturing to ensure manufactured components and systems functioned as planned.

Testing was first performed on the pneumatic actuators to obtain performance capabilities needed to set other design criteria. Testing consisted of manufacturing a rough model functionally identical to the actual design. Numerous tests were performed with the actuator model by launching various weights at varying pressures and recording the varying launch heights. The test data formed a consistent linear fit, and the required pressure to reach the required height of 1 meter was predicted. The required pressure predicted from experimentation consistently read about 30% above the calculated values, likely due to fluid flow inefficiencies and friction. Figure 6 shows this test data.

Drive testing was done to verify that power could

successfully be transmitted from the batteries to the track system. The three AA battery packs were found to supply the motors with sufficient current, and a fourth battery pack did not add any visual benefit.

The three different power transmission systems were also tested: gears, belt drive, and chain drive. Gears required high precision to mesh properly, and there were concerns that the plastic gears teeth might shatter during impact. The belt drive worked, but did not provide the necessary grip when placed under high-torque situations. The chain drive was selected after numerous successful tests.

The track system for the wheels was also fine tuned during the drive test. It was noticed that minute changes in the wheel placement had dramatic effects on the tracking system alignment. Spacers were added to either side of the wheel to aid in keeping the tracks aligned and seated.

The climb tests were performed to find the rover’s maximum angle of attack. After each successful test, the angled surface was set to a steeper angle. Discrepancies

Figure 5: CAD model of the rover with select components removed to show the frame details

Figure 6: Pneumatic Actuator test data and


between the measured motor torque and the manufactures claim, along with a heavier than expected rover weight limited the climbing angle to between 15º and 20º; far short of the goal of 45º.

Pressure testing was performed on the air tanks to ensure that they could withstand pressure up to 100 psi and possible impact loading. Testing was carried out by inflating the pressure tanks to excessive pressures, and subjecting the tanks to significant impact loads by repeatedly hitting the bottle with a 10 foot steel rod. The bottle never exploded, but the cap failed at higher pressures as seen in Figure 7. Epoxy has since been added to the cap to increase strength.

Post-assembly tests consisted of drop testing,

climbing, and jumping. The drop test consisted of a three foot drop with the rover at varying orientation onto a tile floor. With the exception of minor frame deformation when landing from its known worst possible orientation, all tests were successful. The deformation was minor, and future landings in this orientation are extremely unlikely.

The jump test reached just over two feet at ninety-five psi shown in Figure 8. While the expected height was closer to 3 feet, the jump tests were preliminary and minor modifications between the initial tests and final assembly should increase the jump height about six more inches, bringing us closer to the one meter (three foot) goal.

5. Conclusions

During the designing, manufacturing, and testing of the rover, much was learned about what it takes to employ a pneumatic jumping mechanism. After completing the project, there is enough empirical evidence to argue that pneumatics actuators are indeed a practical means of dislodging Mars rovers. With the budget and time allotted, this rover prototype is a simplified demonstration of how such a system would work. By demonstrating how a thirty pound rover can jump over two feet on earth with one hundred psi and two actuators, it can be extrapolated and inferred what a similar system would look like on larger applications. By making a few hypothetical design decisions, the mass a rover that could successfully employ a pneumatics system on Mars could be estimated. Assume the following occurs in order to accommodate a larger rover:

1) A rover only needs to “jump” 6 inches to become dislodged.

2) The rover is jumping on planet Mars, with 1/3 the gravity of earth.

3) Four actuators are used, instead of two. 4) Each actuator is double the size of the current

actuators. 5) The tank pressure is 4500 psi (the pressure of

many carbon fiber high pressure tanks) With these assumptions in addition to the

experimental tests that yielded a linear relationship, the allowable rover weight to successfully use this setup can be extrapolated to over 60,000 lbs. That is,

(4 times less jump height) * (3 times less gravity) * (2 times the number of actuators) * (2 times the size of the actuators) * (45 time the pressure) = 2160 times experimental rover’s weight! That comes out to 2160*30 lbs = 64800 lbs.

Figure 8: Rover beginning to lift off the ground during a jump test.

Figure 7: Air tank trajectory for the first quarter second after cap failure.


The basic design without modifications could propel the 400 lb Sprit and Opportunity rovers to a height of just over 5 inches with the help of Mars’ low gravity. Such a jump would likely be enough to dislodge the rover from a stuck position.

(3 times less gravity) * (24 inches on earth) * (30lbs experimental rover / 400lbs Spirit Rover) = 5.4 inches

6. Improvement Suggestions Based on Tests

After the completion of experiments and the design process, the original design was not the most ideal option for employing a pneumatically actuated system in a Mars rover. The original design has shown that using pneumatic actuators to launch the rover is a viable option, which was the purpose of this prototype, but in order to get a feel of real applications, a new prototype would need to be manufactured utilizing the following improvements:

1. Lighter weight, non-electrical conductive materials. A lighter design would be more beneficial in reducing required inputs to get the desired output, which would allow for the addition of payloads to the chassis.

2. A new chassis design consisting of an improved suspension system. The current system doesn’t protect the drive motors at all. In addition to the motor issues, testing results yielded that the rover lands approximately flat relative to the launch surface 90% of the time. The majority of the current suspension system was designed to allow for in flight reorientation and landing, which means the majority of the current suspension system is rarely utilized.

3. The containment area used in housing electronics and pneumatics would need to be enclosed and ideally combined into one unit instead of two. It would be beneficial to the pneumatic system if the majority of the pneumatics could be run inline instead of jumping to odd orientations in order to minimize tubing necessary to transport high pressure air.

4. The application and use of CO2 gas should be employed instead of compressed air, with possible research into liquid CO2 or dry ice as propellant, which means introducing thermal insulation or even thermal heating, into the pneumatic line to keep the CO2 from freezing when released from a pressurized container.

5. Large improvements can be made to the electrical system including the addition of solar panels to charge batteries, use of pressure and temperature sensors to regulate gas pressure and

consistency, range, tilt, and acceleration sensors to better control pneumatic launches and landings, and integrating all of this into an autonomous system.

7. Benefits to NASA Community

The completion of this objective has shown that pneumatic systems could be practically employed in larger applications with the use of higher tank pressure in conjunction with more and/or larger actuators. In addition to the ability to get rovers dislodged from rough terrain, the ability to trigger a pneumatic launch while in driving motion and clear obstacles also has certain appealing aspects such as the ability to gain access to low level mesas, plateaus and buttes currently inaccessible to present day rovers. Looking beyond the rover application, the integration of pneumatic actuators into new Mars missions would be advantageous. Making pneumatic actuators an addition into human controlled space suits would allow the controller the ability to gain access to and explore low level or large obstacles with a couple of well placed jumps instead of trying to hike around and find a suitable climbing path, which would increase exploration range and better utilize exploration time. 8. Lessons Learned

If the opportunity to redo this experience was presented, less weight would provide more options with better results. Carbon fiber and high density polyethylene were not used for the frame, which would have significantly reduced the weight, due to a lack of knowledge and experience with these materials. Given a 10 week project schedule, it was not feasible to gain the required knowledge of the materials or the skill set to work with the materials. With a lower frame weight the team could have employed smaller motors, actuators, used smaller, low pressure tubing, producing an overall smaller product thus reducing the weight and increasing performance. The reduction in weight would allow for a reduction in required air pressure to achieve the desired results along with a reduction of impact forces on landing which would have been extremely beneficial.

Another lesson learned would be to design the subsystems layout for the pneumatic system and electrical systems before or at least in conjunction with the design of the chassis. One of the largest problems we encountered was trying to integrate subsystems into an arbitrarily set amount of space when the parts ordered after design didn’t fit well into the allotted volume.


9. Rover Upgrades to Date Since the completion of the original prototype shown

in figure 9, Frogger, in comparison, has seen a complete redesign as seen in figure 10. The steel and aluminum frame has been replaced with high density polyethylene and ultra high molecular weight polyethylene. These plastics were chosen due to their relatively high tensile strength as well as their flexural strength. The increased flexibility of the frame allows it to work as the suspension system. This allows the internal systems to be directly attached to the frame. See figure 11. In addition the track system has been removed and replaced with a four wheel drive system. Figure 12 shows the redesigned pneumatics system which has been modified to run inline utilizing pipes instead of tubing to increase the reliability of the system as well as the functionality of the cylinder rotation. Figure 13 show the updated cylinders themselves, which have been redesign using UHMWPE instead of stainless steel for the casing. A half inch diameter titanium piston rod replaced the old quarter inch 1018 steel rod, and again the piping replaces the old tubing. The electronics use a fully digital remote control to reduce the number of misfires that occurred from using a mixed digital/analog controller. The principal components have been removed from the original rover and are ready to be mounted in the newly upgraded Frogger which is currently in the process of being machined.

Figure 9: The origanal rover assembly.

Figure 10: The current Frogger design.

Figure 11: Notice the four wheel drive system and the three point corner braces for the suspension system.

Figure 12: The pneumatics system is now run inline improving efficiency, and actuator motion.

Figure 13: Upgraded pneumatic cylinder. Utilizing pipe instead of tubing, and a titanium pistion for a better weight to strength ratio.

10. References [1] E.Oberg, F.D. Jones, H.L. Horton, and H.H. Ryffel, 27Machinery’s Handbook, Industrial Press, New York, 2004.


11. Appendices

Frame Strength: Assumptions: Dtube 0.75in

ttube 0.0625in

Ltot 16in

Fmax 151lbf

Lbeam 20in

Calculate the Bending Stress:

Mbend ymax

I Find Bending Moment:

Mbend

Fmax

2

Lbeam

2

Mbend 755 lbf in

Find Moment of Inertia:

I

64Dtube 4 Dtube 2 ttube

4

I 0.008041in4

Find "y max":

ymax

Dtube

2

ymax 0.375 in

Determine Bending Stress: y_alum 21000psi

y_steel 63250psi

max

Mbend ymax

I

max 3.521 10

4 psi

0.931 0.593 0.338

SFalum

y_alum

max

SFsteel

y_steel

max

SFalum 0.596

SFsteel 1.796


Determine Weight:

steel 0.23lbm

in3

alum 0.0975lbm

in3

Find Cross Sectional Area:

Across_sec_tube

4Dtube 2 Dtube 2 ttube

2

Across_sec_tube 0.135 in2

Find the Total Frame Weight: Wtot_alum alum Across_sec_tube Ltot

Wtot_steel steel Across_sec_tube Ltot

Wtot_alum 0.211lb

Wtot_steel 0.497lb

Determine Strength To Weight Ratio:

SWRalum

y_alum

alum

SWRsteel

y_steel

steel

SWRalum 5.775 105

ft

2

s2

SWRsteel 7.373 105

ft

2

s2

Spring Calculations:

Longitudinal Springs Calculation: Assumptions:

k 51lbf

in

xfree 4.18in xsolid 2.1in mtot 12lbm

Nsprings 4 <--Number of springs in the direction of impact (total longititudinal springs is double this)

mper_spring

mtot

Nsprings mper_spring 3 lbm

Variables: xprecomp 3.35in


Calculate Drop Height (Using Energy Method): *** There will be a "limiter" that prevents the opposing spring from pushing in the direction of impact. (Undesirable).

m g h1

2k xf

2xi

2

2.5 g h

1

2k xfree xsolid 2 xfree xprecomp 2

h

1

2k xfree xsolid 2 xfree xprecomp 2

mper_spring g h 2.577 ft

Calculate Drop Height (Using Kinematic Equations):

Favg

k xf x i 2

Favg

k xfree xsolid xfree xprecomp

2

Favg m aavg Favg 74.205lbf

aavg

Favg

mper_spring aavg 795.825

ft

s2

aavg_spring aavg aavg_spring 242.567m

s2

V 2 a s Vspring Vfall

2 aavg_spring sspring 2 agravity sfall aavg_spring xprecomp xsolid g sfall

sfall

aavg_spring xprecomp xsolid

g sfall 2.577 ft

Calculate Maximum G-Forces Frebound k xfree xsolid Frebound 106.08lbf

F m a

arebound

Frebound

mper_spring arebound 1.138 10

3

ft

s2

Gsarebound

g Gs 35.36


Actuator Pressure Calculations: xfall 1m "Fall" height and/or jump height

g 9.807m

s2

Force of gravity

xtakeoff 4in Stroke of the actuator (length of acceleration)

mass 20lbm Mass launched per actuator per cylinder Dpiston 1.875in Actuator piston diameter

x xo v0 t1

2a t

2 General Kinematic Equation Eqn. 1

xfall1

2g tfall

2 Initial x and v equal zero, and are removed. a = gravity

tfall

2xfall

g Previous equation (Eqn. 1) rearranged

tfall 0.452s The time it would take to fall from the "fall" height and/or jump

height v a t General Kinematic Equation Eqn. 2 Vfall g tfall Equation 2 with gravity substituted for the acceleration

Vtakeoff Vfall

The initial velocity of launch will equal the velocity at the end of the

fall

Vtakeoff 4.429m

s The required takeoff velocity to reach the predetermined jump

height

v2

v02

2 a x General Kinematic Equation Eqn. 3

Vtakeoff2

2 atakeoff xtakeoff The initial velocity is equal to zero and was removed

atakeoff

Vtakeoff2

2 xtakeoff The previous equation (Eqn. 3) rearranged

This is the acceleration required to achieve the required velocity in the predetermined actuator stroke distance.


atakeoff 96.522m

s2

F ma Newton's Second Law Eqn. 4 Ftakeoff mass atakeoff Substitution of Variables into Eqn. 4

This is the constant force required to accelerate the predetermined mass to the calculated force in order to achieve the predetermined height.

Ftakeoff 875.634N

Factuator Ftakeoff mass g The actuator force must also overcome the Force of gravity to lift

the predetermined mass against gravity.

Factuator 964.599N This is the force that the actuator must supply to accelerate the

predetermined mass to the calculated force in order to achieve the predetermined height.

A D

2

4 Equation for the area of a Circle Eqn.5

Apiston

Dpiston2

4 Eqn. 5 rearranged

Apiston 2.761 in2

This is the area of the piston

Pactuator

Factuator

Apiston Pressure Equation Eqn. 6

Pactuator 5.415 105

Pa This is the pressure required to launch the predetermined mass to

the predetermined height. (With experimental actuator's specs) Pactuator 78.536psi


Pneumatic Cylinder Failure Calculations: Goal: Verify the structural integrity of the pneumatic actuator by performing failure analysis calculations for all anticipated modes of failure. Possible Modes of Failure: 1) Cylinder Bursts 2) Tie Rod Yielding Due to Tension 3) Top of Cylinder Shears Due to Impact 4) Threads Strip *Fatigue is taken into account in the safety factor. Under 1000 cycles, 90% of the initial strength of the material is retained, making fatigue calculations negligible.

CylinderTop

FAxialMax

Ashear

Impulse Calculations (to be used in failure analysis): Assumptions (worst case): mLaunchStructure 0.5lbm Per cylinder.

hjump 1m

xaccel1

8in 1 1/8in washer and one 1/16in washer (assuming not fully

compressed, that is why we use 1/8, not 1/8 + 1/16) Find Takeoff Velocity:

Vtakeoff2

2 g hjump

Vtakeoff 2 g hjump

Vtakeoff 4.429m

s

Find Acceleration of Launch Structure:

Vtakeoff2

2 aLaunchStructure xaccel

aLaunchStructure

Vtakeoff2

2 xaccel


aLaunchStructure 3.089 103

m

s2

Find the Force (per cylinder) Due to Impulse of Launch: FAxialMax mLaunchStructure aLaunchStructure

FAxialMax 0.701 kN

FAxialMax 157 lbf PER CYLINDER

1) Cylinder Burst - Failure Analysis: Assumptions (worst case): Cylinder will initially be under compression; however, this was neglected because the worst case will occur when the cylinder is loaded in tension.

twall1

16in

SteelYield 234MPa <--- Stainless Steel 302A (A weaker steel)

Pmax 200psi

rcylinder 0.9375in

Thin-Wall Cylinder Equation for Hoop Stress:

hoop

Pmaxrcylinder

twall hoop 20.684MPa

Axial Cylinder Stress: rinner rcylinder

router rcylinder twall

ACylinderCrossSection router2

rinner2

CylinderAxial

FAxialMax

ACylinderCrossSection

CylinderAxial 2.854 MPa


Von Mises Stress: 1 hoop <--------------- Negative because 1) quantitatively, von

Mises stress is less than the axial cylinder stress if it is positive, and 2) qualitatively, because the pressure pushing outward on the cylinder is creating stress in compression in the axial direction (compression is negative, tension is positive).

2 CylinderAxia

e 12

22

1 2

e 22.249MPa

Calculate the Safety Factor Using Maximum-Distortion-Energy Theory (von Mises):

SFcylinder

SteelYield

e SFcylinder 10.517

2) Tie Rods Yielding - Failure Analysis: Assumptions (worst case): NumberOfRods 4 Drod 0.125in

Stainless Steel 302A Rods ---> Defined Above Force Per Rod Using the Maximum Axial Force Due to Impulse from Takeoff: 2 times the maximum axial load because the rod will initially be preset in tension to a value that is near the maximum axial load in order to avoid leakage during the small periods of time when the actual load is applied. Ideally, the value would be at least 2x, but it is unlikely that this will actually be true. 2x is probably a safe number, it will likely have lower initial tension.

FRodMax

2FAxialMax

NumberOfRods FRodMax 0.35 kN

Cross Sectional Area of the Tie Rods:

Arod Drod

2

4 Arod 7.917 10

6 m

2

Maximum Axial Stress of the Tie Rods:

rods

FRodMax

Arod rods 44.239MPa


Calculate the Safety Factor of the Tie Rods:

SFrods

SteelYield

rods SFrods 5.289

3) Top of Cylinder Shear Yielding - Failure Analysis: Assumptions (worst case): AlumYield 110MPa Aluminum Alloy 6061-T4

tshear1

8in

Shear Strength of Aluminum: AlumYield 0.55AlumYield AlumYield 60.5 MPa

Shear Area:

Ashear 2 rcylinder tshear Ashear 4.75 104

m2

Shear Stress: CylinderTop 1.475 MPa

Calculate the Safety Factor of the Top of the Cylinder:

SFshear

AlumYield

CylinderTop SFshear 41.027

4) Thread Stripping - Failure Analysis: Similar to Tie Rod calculations, we will use a value of 2x the maximum axial force to represent a static force on the threads. This value is chosen because the rod will be under an initial tensile force in addition to the maximum axial force from the impulse of takeoff. Assumptions (worst case): Stainless Steel 302A Rods and Nuts ---> Defined Above Nrods 4 <-- Number of Tie Rods

http://www.rjleahy.com/Techcenter/nuts/hex_nuts.htm "Square and Hex Machine Nuts - Size No. 5

tnut 0.102in Specs for UNC No. 5 (D=0.125") Class 2A threads -

(Machinery's Handbook):

pcoarse1

40in

do 0.1242in

di 0.1191in


Stress on threads:

threads

4 2FAxialMax

Nrods

do2

di2

pcoarse

tnut Eqn. 10.10 in Machines Book

The "2" is explained above. threads 136.538MPa

Calculate the Safety Factor of the Threads:

SFthreads

SteelYield

threads SFthreads 1.714

Conclusion (Before changes of launch structure weight and extra rubber washer thickness): The chosen materials and thicknesses are probably sufficient; however, to maximize strength, the following should be done (in order of importance). 1) Add extra-thick rubber washers to minimize the maximum axial force! (VERY IMPORTANT) 2) Minimize the weight of the launch structure to minimize axial force. 3) Increase the shear thickness on the top of the cylinder. 4) Increase the thickness of the tie rods if need be (however, this will add weight). 5) Increase the threaded thickness (or number of nuts) if need be. 6) Using higher quality materials or adhering to more realistic assumptions will help the safety factors all around. The safety factors shown are Worst Case. THICK RUBBER WASHERS IS, BY FAR, THE MOST IMPORTANT!


Motor Calculations: Design Constraints: Wtot 30lbf Dwheel 8in

Calculate Stall Torque Required to Climb a Vertical Wall: We are calculating this unrealistic situation so that we can be positive that the rover will not be short of the required torque. Assumptions: Nmotors 2 <-- Number of Motors

Calculations:

rwheel

Dwheel

2

Fclimb Wtot Fclimb 133.447N

Ttot rwheel Fclimb Ttot 13.558N m

Tstall

Ttot

Nmotors Tstall 6.779 N m

Tstall 5 ft lbf

Tstall 960 ozf in Ounce-force * inch PER MOTOR

Calculate the Maximum Endurance and Range of the Motor: Assumptions: Qbattery 5A hr

Inominal 0.1A <--- "Nominal" Current Draw per motor

Endurance Calculations: Itot Inominal Nmotors Itot 0.2A

IQ

t

tQbattery

Itot t 25 hr

Design and Fabrication of Pneumatically Actuated Mars ...

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